page_title: Einzel lens
section_title: Theory
hierarchical_section_title: Einzel lens / Theory
caption_attribution_description: Español: Esta imagen muestra una simulación del camino que siguen los iones cuando viajan por una lente de Einzel. La masa del ion es 200kDa acelerada a 40kV, el potencial de la placa media está en 200V y el tamaño de la placa es 1 metro (estos son ajustes muy grandes que suelen mostrar el efecto enfocado más fácilmente; pero no son ajustes prácticos). English: This shows the path of ions as they travel through a simulated Einzel lens. The ion mass is 200kDa accelerated to 40kV, the middle plate potential is at 200V and the plate size is 1m – these are very large settings used to show the focusing effect more easily and are not practical settings.
context_page_description: An einzel lens, or unipotential lens, is a charged particle electrostatic lens that focuses without changing the energy of the beam. It consists of three or more sets of cylindrical or rectangular apertures or tubes in series along an axis. It is used in ion optics to focus ions in flight, which is accomplished through manipulation of the electric field in the path of the ions.
  The electrostatic potential in the lens is symmetric, so the ions will regain their initial energy on exiting the lens, although the velocity of the outer particles will be altered such that they converge on to the axis. This causes the outer particles to arrive at the focus intersection slightly later than the ones that travel along a straight path, as they have to travel an extra distance.
context_section_description: The equation for the change in radial velocity for a particle as it passes between any pair of cylinders in the lens is:
  with z axis passing through the middle of the lens, and r being the direction normal to z.  If the lens is constructed with cylindrical electrodes, the field is symmetrical around z.   is the magnitude of the electric field in the radial direction for a particle at a particular radial distance and distance across the gap,  is the mass of the particle passing through the field,  is the velocity of the particle and q is the charge of the particle. The integral occurs over the gap between the plates. This is also the interval where the lensing occurs.
  The pair of plates is also called an electrostatic immersion lens, thus an einzel lens can be described as two or more electrostatic immersion lenses.  Solving the equation above twice to find the change in radial velocity for each pair of plates can be used to calculate the focal length of the lens.
caption: Path of ions as they travel through an einzel lens. The ion mass is 200 kDa accelerated to 40 kV, the middle plate potential is at 200 V, and the plate size is 1 m (note that these values are atypical for illustrative purposes).
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